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  4. A running track of 440 m is to be laid out enclosing a football field, the shape of which is a rectangle with semi circle at two opposite end. If the area of the rectangular portion is to be maximum, then the length of its sides is

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Q. A running track of $440\, m$ is to be laid out enclosing a football field, the shape of which is a rectangle with semi circle at two opposite end. If the area of the rectangular portion is to be maximum, then the length of its sides is

Application of Derivatives

Solution:

$2 \ell+2 \pi r=440$
$A =\ell 2 r=-2 \pi r^2+440 r$
$\frac{ dA }{ dr }=-4 \pi r +440=0$
image
at $ r =110 \,m , \frac{220}{\pi} m$